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Monday, January 23, 2012

In which Ashes is recorded for future use

This is apropos of nothing, but this idea has been worked into my mind and I feel like recording it here, because it might have some future use. Or not. It's here, either way. It's a simple system I call "Ashes", based on its two main symbols, the dash and the asterisk.

The rules are as follows:

-- is a valid sequence

** is a valid sequence

You can add - to the end of a valid sequence ending in --

You can add * to the end of a valid sequence ending in **

If you have a valid sequence composed entirely of asterisks, and a valid sequence composed entirely of dashes, you can insert a copy of the dashes sequence between every asterisk of the asterisk sequence

If you have a valid sequence that contains the fragment -*-, you can add # to both ends and remove all the asterisks.

You'll notice you can have sequences of any length greater than 1, as long as they are composed entirely of dashes or entirely of asterisks, thanks to rules 1-4. For example:
---
-----
-------
*****
***
**

Rule 5 allows you to combine them. For example, combining the first and the fourth would result in

*---*---*---*---*
You could use the second with the fifth and the third with the sixth, getting

*-----*-----*

*-------*

And so on and so forth.

Rule 6 is the closer, where the # symbol appears. Using it with those above we would get

#------------#

#----------#

But we cannot use rule 6 on *-------* to get #-------#, because at no point does -*- appear in *-------*.

There is a reason behind this bizarre set of rules, of course, some interesting property behind the chains that can and can't appear. It seems obvious to me, actually, but that's probably because I thought it up so it would fulfil that express purpose. I suspect it is not immediately clear to most other people. It might be a fun riddle, I don't know.